Subgame Perfect Punishment for Repeat Offenders

First we show that for wealth-constrained agents who may commit an act twice the optimal sanctions are the offender's entire wealth for the first and zero for the second crime. Then we ask the question whether this decreasing sanction scheme is subgame perfect (time consistent), i.e., does a rent-seeking government stick to this sanction scheme after the first crime has occurred. If the benefit and/or the harm from the crime are not too large, this is indeed the case; otherwise, equal sanctions for both crimes are optimal.